The Expressive Power of Valued Constraints: Hierarchies and Collapses

Abstract. In this paper we investigate the ways in which a fixed collection of valued constraints can be combined to express other valued constraints. We show that in some cases a large class of valued constraints, of all possible arities, can be expressed by using valued constraints of a fixed finite arity. We also show that some simple classes of valued constraints, including the set of all monotonic valued constraints with finite cost values, cannot be expressed by a subset of any fixed finite arity, and hence form an infinite hierarchy.

• Type: Conference
• Year: 2007
• Where: CP
• Authors: David A. Cohen, Peter Jeavons, Stanislav Zivný
• Keywords: Artificial Intelligence, CP 2007, Finite Arity, Fixed Collection, Monotonic Valued Constraints